Computer Tomography (CT) systems have enabled physicians to perform noninvasive examinations and glean information about the patient by obtaining a cross-sectional view of the patient. The quality and reconstruction speed have improved dramatically over the years. Simultaneously, wider recognition of the value and potential of CT systems as well as declining costs have contributed to dramatic growth in the industry. Although CT systems have witnessed significant increase in market penetration, the untapped potential is enormous. In order to tap the market further, both costs and performance characteristics have to improve. Recent attempts to meet these needs have led, for example, to the development of videographic tomographic techniques based on the convolution back projection algorithm. Although the design of systems that can generate images at frame rates (30 frames per second) using the technique are now feasible, the method suffers from several disadvantages. The disadvantages include:
High costs due to the need for using expensive high speed filters. PA1 Distortion introduced by the high speed filter, optical devices and prism image rotator.
Commonly used tomographic algorithms can be broadly classified as direct and iterative methods, based on the method of computation. When a system is underdetermined, commonly used iterative algorithms, such as the Simultaneous Iterative Reconstruction Technique (SIRT) do not guarantee a unique solution. The Projection Iterative Reconstruction Technique (PIRT) proposed in the present invention is a basic iterative image reconstruction algorithm which can be considered as a counterpart of the conventional algorithm--SIRT. The PIRT attempts to obtain the minimum-norm solution of an underdetermined system, whereas, conventional methods are usually based on an attempt to estimate the least squares solution of an overdetermined system. Therefore, when the PIRT algorithm is applied to an underdetermined system, a unique solution is intrinsically guaranteed. The proposed algorithms include a family of accelerated algorithms, such as PIRT-CG (PIRT--Conjugate Gradient), and PIRT-PC (PIRT--Partial Convolution).
A 2-D cross-sectional image of a 3-D object is shown in FIG. 6. Parallel x-ray projections are taken around the object in several orientations. The objective of the tomographic image reconstruction algorithm is to reconstruct the 2-D cross-sectional image on the basis of information contained in the ray-sums of projections measured from several orientations across the image plane around the object.
In the continuous case, a ray sum is expressed by the Radon transform which is obtained by performing a line integration along each ray. As shown in FIG. 7, a line integral P.sub..theta. (t) can be defined as ##EQU1## Using the sifting property of the delta function, eq. 5 can be rewritten as ##EQU2## The function P.sub..theta. (t) is known as the Radon transform of the function f(x, y).
In the discrete case, eq. 6 can be rewritten in the form of a summation and projection operations can be modeled using a linear system representation EQU Ax=b (3)
where x represents all pixels on the two dimensional image, b represents data measured at all projection orientations, and the matrix A maps data from the image space to the projection space. Image reconstruction involves estimation of the 2-D image x from known projections b.
Tomographic image reconstruction involves operations of mapping the data from the projection space back to the image plane. The operation is called back projection. The back projection was one of the earliest methods used to obtain the a cross-section of an object in an x-ray film before computed tomography was invented. Since the method simply smears the projection data back to the image space instead of solving for the true inverse, information in the reconstructed image severely lacks in detail.
Tomographic image reconstruction involves estimation of f(x, y) from given P.sub..theta. (t) using the inverse Radon transform. The task is summarized in eq. 6 for the continuous case. In the discrete case, the objective is to determine x from known b as expressed in eq. 7. In computed tomography, the enormous amount of data contained in the projections collected in several directions has to be appropriately manipulated to obtain the spatial distribution of the parameters. The algorithms for tomographic imaging solves the inverse problem by estimating the cross-sectional images from the given projections.
In the case of most iterative reconstruction methods, the error corrections are fed back in the image space except for a few exceptions, such as the Projection Space Iterative Reconstruction-Reprojection (PIRR) and Projection Space MAP (PSMAP) methods. The PIRR projects the reconstructed image to the projection space recursively in order to recover the missing projection data whereas the PSMAP optimizes data in the projection space iteratively and then reconstructs the image using convolution back projection (CBP). The approaches and objectives of the projection space iterative algorithms differ from the PIRT proposed in the present invention.
Because of the extreme computational demands, iterative methods usually are not able to compete with direct algorithms in commercial CT systems. However, the iterative algorithms still offer advantages in certain applications. They are particularly suitable for reconstructing images from incomplete data, reconstruction with a priori statistical knowledge as well as single photon emission computerized tomography (SPECT) and positron emission tomography (PET).
As mentioned before, conventional x-ray tomography techniques were used to estimate cross-sectional images of objects even before the invention of computed tomography. In this method, a photographic film and the object are rotated synchronously. X-rays pass through a narrow slit, penetrate the object and are recorded on the film. The signal is then smeared on the film plane. Although, the technique may be considered as the earliest optical implementation of tomography, the method is mathematically equivalent to the back projection method. However, the quality of results obtained are poor compared with those obtained using modern computed tomography techniques.
The computed tomography methods differ from the conventional tomography schemes in that they attempt to solve the inverse problem using the measured projection instead of simply smearing the projections back into the image space.
The earliest reported optical computed tomographic reconstruction processor was built by Peter in 1973. An image was first recorded on a film using back projections. The output image was obtained by filtering the blurred image using a coherent optical spatial filter. The resulting image was much sharper than those obtained using back projections only.
In order to avoid the problems associated with coherent processing such as speckle and other coherent noise, several incoherent optical tomographic reconstruction systems were built.
The Oldelft transaxial tomography system, built in 1978, implements the convolution back projection method. The Oldeft system is a hybrid system and optics is used only for one dimensional and two channel convolutions. The two channels are used for positive and negative valued convolution respectively.
The Edholm's system, built in 1977, is an optical system using films. The original projections and the filtered negative projections are prepared on two separate films. The reconstructed image is then recorded on a rotating output film.
Since 1977, several structures have been proposed by Gmitro et al. where pupil plane masks have been used for spatial radius filtering operations. This approach, known as optical transfer function (OTF) synthesis, is a technique for performing spatial filtering operations in an incoherent system. The loop processor records all projections on a continuous film loop and the drum processor records projections on the surface of a drum. The CCD processor collects the back projected output image using a CCD camera.
Several coherent computed tomography systems have been proposed by Hansen et al., and Nishimura and Casasent. These approaches have been summarized by Gmitro et al. All of these algorithms involve the use of direct algorithms. Due to the finite dynamic range of materials and devices, and distortions of optical transforms, these approaches could not compete with electronic computers in respect of the quality of reconstructed images.
Advances in technology related to video imaging devices have led to improvements in the quality and speed of optical implementations. Recently, a videographic tomographic structure for medical imaging, built by Gmitro et al., was able to achieve 1% contrast resolution. The structure was able to achieve real time reconstruction. Three filter structures were evaluated including a digital FIR filter, an Acoustic-optic (AO) convolver and a Surface Acoustic Wave (SAW) convolver. The best results were obtained using the digital FIR filter. However, the digital FIR filter was not only expensive but also introduced distortions in the low frequency range since the order of the filter used was not long enough to cover the entire frequency range. In addition, optical distortions were not eliminated. Nevertheless, the development is very encouraging since it demonstrated the feasibility of high quality and high speed optoelectronic tomography.
The present invention provides a new approach/structure for tomographic reconstruction. The basic structure is built from optoelectronic devices and allows for implementation of a number of reconstruction algorithms. The critical devices used in this structure are Spatial Light Modulator (SLM) and Charge Coupled Device (CCD) arrays which are commonly used as liquid crystal television display panels and solid state video image detectors, respectively.
Spatial Light Modulators (SLM's) are devices which can be employed to modulate the intensity, magnitude, polarization or phase of light. Applications of SLM range from commercial television displays, real-time image processing to parallel optical computing. FIG. 8 shows an example of a linear SLM array with four cells. The optical transmissivity of each cell can be controlled by the applied modulating signal. The intensity of the output light beam from each cell is, therefore, a function of the intensity of the incident beam and the transmissivity of the cell. SLM's can be classified on the basis of their addressing modes. If the modulating signal is controlled by an electrical signal, it is referred to as an electrically addressed SLM (E-SLM). If the modulating signal is a second beam of light, it is classified as an optically addressed SLM (O-SLM).
SLM's have been built using several technologies. This had led to the development of the optoelectronic SLM, opto-acoustic SLM, and opto-magnetic SLM. Commercially available SLM's, such as Liquid Crystal (LC) SLM, and Ferroelectric Liquid Crystal (FLC) SLM will be briefly described in this section. For the sake of completeness, Multiple Quantum Well (MQW) SLMs are also discussed.
Liquid crystals are organic materials that possess an intermediate phase between the solid and liquid phase. The molecular orientations of liquid crystal materials can be changed by applying electrical fields. Therefore, the polarization of the light through such materials can also be twisted. Amplitude and intensity modulation is obtained by placing a polarizer and an analyzer in front of and behind the liquid crystal layer respectively. The technology relating to Liquid Crystal SLM has been used in commercial video image projectors and miniature television sets. Since commercial LCTV's offer many of the same attractive features as other modulators, but at only a fraction of the cost, they have also been used in many optical signal processing and computing systems.
Ferroelectric liquid crystals are characterized by a spontaneous molecular polarization caused by an anisotropy in the molecule. The molecular polarization allows the orientation of FLC's to be easily switched with a small electric field. The FLC SLM has the advantage of high speed and high contrast ratio. Commercial available FLC SLM only offer binary light modulation since tilting of FLC molecules is confined to two orientational positions.
Multiple quantum well (MQW) structures consist of thin layers of low bandgap semiconductor (wells) sandwiched between layers of larger bandgap semiconductor (barriers). When the thickness of the well layers is on the order of a carrier de Broglie wavelength, the electron and the hole are forced to orbit close to each other and the binding energy increase correspondingly. The electrical and optical properties of the structure are then dominated by quantum size effects (QSE). The QSE results in the features of step-like absorption edges in the optical absorption spectrum and room temperature exciton resonances. The change in the energy levels of the excitons resulting from applied electric field, called the quantum-confined Stark-effect (QCSE), allows shifting of the abrupt, highly absorbing edge. By shifting the absorption edges, the MQW structures produce larger absorption changes (in a narrow spectrum range around the absorption edges) than those in bulk semiconductors with the same applied field.
The LCTV's are able to provide better grey level images. However most of them can only operate at television frame rates (30 to 60 frames per second). The FLC SLM's support binary processing only but can operate at relatively higher speed (up to 100 Khz). The MQW SLM's are expected to operate at GHz rates. However, the spectrum of modulated light has to be within a narrow range.
TABLE 1 __________________________________________________________________________ Characteristics of Several Common SLMs SLM Visibility Resolution Size Speed Cost __________________________________________________________________________ MSLM 0.5 4 lp/mm 25 mm dia 2 sec $25K MOD 0.91 6.4 lp/mm 1 .times. 1 cm 200 Hz $18K DMD 0.5 10 lp/mm 0.64 cm 60 Hz ? FELC 0.9 40 lp/mm 12.5 mm dia 60 Hz $17.5K HC LCLV 0.86 60 lp/mm 50 .times. 50 mm 60 Hz $25K Epson 0.96 6.3 lp/mm 2.54 .times. 1.9 cm 60 Hz $800 LCTV __________________________________________________________________________
TABLE 2 __________________________________________________________________________ Specifications of Several Electrically Addressed SLMs frame pixel fill contrast device material pixels rate Hz size .mu.m factor ratio __________________________________________________________________________ STC Ltd. FLC 128 .times. 128 165 165 .times. 165 0.83 200:1 Displaytech FLC 10 .times. 10 2000 1.sup.3 .times. 10.sup.3 0.77 100:1 Disp.tech FLC 64 .times. 64 4500 45 .times. 45 0.56 12:1 CMOS Semetex SMD Iron 128 .times. 128 100 56 .times. 56 0.54 10.sup.4 :1 Garnet Litton Iron 128 .times. 128 2000 56 .times. 56 0.54 -- MOSLM Garnet TI DMD Def.mirr 128 .times. 128 1200 25 .times. 25 0.9 2:1 or __________________________________________________________________________
Charge Coupled Devices (CCD) are also called Charge Transfer Devices (CTD). These devices were introduced by Boyle and Smith in 1970. The applications of CCD's include optoelectronic computing, charge domain signal processing, focal plane image processing, high speed analog-to-digital and digital-to-analog conversion, time-axis conversion, and image detection.
A CCD array functions like shift registers in which sampled values of an analog signal are stored in the form of charges in a series of neighboring cells. Clock pluses allow the transfer of charge from one cell to the next without significant loss in accuracy. The charge, which is called a charge packet, is a small amount of charge stored in potential wells created by the gate voltage. By periodically varying the electrode or gate voltage, the potential wells are shifted along the semiconductor. The charge packet, located under the voltage gate, moves along with the potential wells.
CCDs can be classified as surface-channel CCD (SCCD) and bulk-channel CCD (BCCD) depending on the device structures. A device is called SCCD if the charge resides at the semiconductor surface. In the BCCD, the charge location is moved away from the surface into the n-channel. There is no interaction between the charge and the interface states. In the case of peristaltic CCD, the n-channel is thicker and the charge is farther away from the surface. In spite of the increased process complexity, almost all of today's devices are BCCD's, due to their superior performance.
High performance Silicon CCDs can offer charge transfer efficiencies as high as 0.999999. Some of the fastest Silicon CCDs have been operated at several hundred MHz. Silicon peristaltic CCDs have been operated with clock frequencies up to 200 MHz. High mobility GaAs is a good material for building very high frequency CCD's. Devices with operating frequency in the range of GHz have been fabricated. However, typical operational frequencies of commercially available Silicon CCD's are usually below 20 MHz.
CCD detecting arrays are commonly used as solid state image detectors. FIG. 9 shows a linear CCD detector array with four cells. Each cell generates an electrical charge proportional to the number of photons incident on it. Alternatively, the charge developed is proportional to the intensity of the light integrated over the period of exposure. Charges in a CCD array can be shifted from cell-to-cell without significant loss in magnitude. The output is a sequence of voltage values proportional to the charge in each cell. Typical contrast resolution of commercial image detectors can be in excess of 4096 distinguishable gray levels.